What do these symbols mean in the report?

I sometimes wonder what the marked symbols mean when I'm looking on a report of a Pokémon. Some of them imply a direct meaning, but I'd rather be sure.

What do these symbols mean and are some of them essential for online competition?

Sample with questioned symbols marked. German localization.

Those symbols are set only by players and is completely up to the player.

There are coincidentally 6 marks (equal to the number of stats: HP, Atk, Def, Sp.Atk, Sp.Def, Spd) you can 'mark' or un-'mark', which can be ideal to mark what stats of a Pokemon are at 31 IVs, which I've found to be the most common use of these.

Of course, it's entirely up to you to decide what to do with them.

You can 'mark' or un-'mark' from the summary page of a Pokemon or through the 'Marking' option in your PC box.